摘要
为了得到半立方、平方、立方抛物线形渠道共轭水深的显式计算公式,对这3种抛物线形渠道的水跃方程进行恒等变形,利用临界水深介于跃前水深和跃后水深之间的性质,得到了无量纲跃前水深x和无量纲跃后水深y之间的关系式,进一步分别得到其迭代公式。在工程常用范围内,利用excel拟合得到其迭代初值,提出了一套抛物线类渠道共轭水深的显式计算公式。最后,实例及误差分析表明:半立方、平方、立方抛物线形断面无量纲跃前水深x、无量纲跃后水深y最大相对误差分别为0.25%,-0.23%;0.17%,-0.29%;0.31%,0.39%。公式物理概念清晰,计算简捷,精度高,适用范围广。
In order to get the explicit calculation formula of conjugate depth for semi-cubic,square,and cubic parabolic-shaped channels,the jump equations of the three parabola-shaped channels were transformed identically and the relationships between the dimensionless water depth x before jump and the dimensionless water depth y after jump were obtained according to the property that the critical depth was between the pre-jump depth and the postjump depth. Their iterative formulas were further obtained respectively. Hence,a set of explicit calculation formulas of conjugate depth for semi-cubic,square,and cubic parabolic-shaped channels were obtained by fitting the iterative initial value through excel in common engineering scope. Finally,example and error analysis shows that the absolute value of maximum relative error of dimensionless water depth x before jump was 0. 25%,0. 17%,and0. 31% respectively for the semi-cubic,square,and cubic parabolic-shaped channel,and that of dimensionless water depth y after jump was respectively- 0. 23%,- 0. 29%,and 0. 39%. The formulas were convenient and highly accurate with clear physical meaning and wide application scope.
出处
《长江科学院院报》
CSCD
北大核心
2015年第8期51-56,共6页
Journal of Changjiang River Scientific Research Institute
关键词
半立方抛物线形断面
平方抛物线形断面
立方抛物线形断面
共轭水深
显式计算公式
semi-cubic parabola-shaped channel
square parabola-shaped channel
cubic parabola-shaped channel
conjugate depth
explicit calculation formula
